Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690831 | C2 | semidirect |
| 2. #20261407 | C2 | semidirect |
| 3. #20261405 | C2 | semidirect |
| 4. #20261111 | C2 | semidirect |
| 5. #20260970 | C2 | semidirect |
| 6. #20260936 | C2 | semidirect |
| 7. #20260881 | C2 | semidirect |
| 8. #20260879 | C2 | semidirect |
| 9. C4×#13095501 | C2 | semidirect |
| 10. #20260800 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 58. #13095501 | D4 | semidirect |
| 130. C4×C97 | #135 | semidirect |
| 143. C97 | #3287 | semidirect |
| 150. #460 | D97 | semidirect |
| 276. C4 | #15690831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| #20261407 | 2 |
| #20261405 | 2 |
| #20261111 | 2 |
| #20260970 | 2 |
| #20260936 | 2 |
| #20260881 | 2 |
| #20260879 | 2 |
| C4×#13095501 | 2 |
| #20260800 | 2 |
| #460×C97 | 2 |
| #3287 | 97 |